9780073251639

0073251631

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Summary

ELEMENTARY STATISTICS: A STEP BY STEP APPROACHis for general beginning statistics courses with a basic algebra prerequisite. The book is non-theoretical, explaining concepts intuitively and teaching problem solving through worked examples and step-by-step instructions. This edition places more emphasis on conceptual understanding and understanding results. This edition also features increased emphasis on Excel, MINITAB, and the TI-83 Plus and TI 84-Plus graphing calculators, computing technologies commonly used in such courses.

Table of Contents

Preface

xi

The Nature of Probability and Statistics

1

(32)

Introduction

2

(1)

Descriptive and Inferential Statistics

3

(3)

Variables and Types of Data

6

(3)

Data Collection and Sampling Techniques

9

(4)

Random Sampling

10

(2)

Systematic Sampling

12

(1)

Stratified Sampling

12

(1)

Cluster Sampling

12

(1)

Other Sampling Methods

13

(1)

Observational and Experimental Studies

13

(3)

Uses and Misuses of Statistics

16

(3)

Suspect Samples

17

(1)

Ambiguous Averages

17

(1)

Changing the Subject

17

(1)

Detached Statistics

18

(1)

Implied Connections

18

(1)

Misleading Graphs

18

(1)

Faulty Survey Questions

18

(1)

Computers and Calculators

19

(5)

Summary

24

(9)

Frequency Distributions and Graphs

33

(62)

Introduction

34

(1)

Organizing Data

35

(13)

Categorical Frequency Distributions

36

(1)

Grouped Frequency Distributions

37

(11)

Histograms, Frequency Polygons, and Ogives

48

(15)

The Histogram

48

(2)

The Frequency Polygon

50

(1)

The Ogive

51

(2)

Relative Frequency Graphs

53

(2)

Distribution Shapes

55

(8)

Other Types of Graphs

63

(23)

Pareto Charts

64

(1)

The Time Series Graph

65

(1)

The Pie Graph

66

(4)

Misleading Graphs

70

(3)

Stem and Leaf Plots

73

(13)

Summary

86

(9)

Data Description

95

(76)

Introduction

96

(1)

Measures of Central Tendency

97

(18)

The Mean

98

(3)

The Median

101

(2)

The Mode

103

(2)

The Midrange

105

(1)

The Weighted Mean

106

(2)

Distribution Shapes

108

(7)

Measures of Variation

115

(18)

Range

116

(1)

Population Variance and Standard Deviation

117

(2)

Sample Variance and Standard Deviation

119

(2)

Variance and Standard Deviation for Grouped Data

121

(3)

Coefficient of Variation

124

(1)

Range Rule of Thumb

125

(1)

Chebyshev's Theorem

125

(2)

The Empirical (Normal) Rule

127

(6)

Measures of Position

133

(19)

Standard Scores

133

(2)

Percentiles

135

(6)

Quartiles and Deciles

141

(1)

Outliers

142

(10)

Exploratory Data Analysis

152

(9)

The Five-Number Summary and Boxplots

153

(8)

Summary

161

(10)

Probability and Counting Rules

171

(66)

Introduction

172

(1)

Sample Spaces and Probability

173

(16)

Basic Concepts

173

(3)

Classical Probability

176

(3)

Complementary Events

179

(2)

Empirical Probability

181

(2)

Law of Large Numbers

183

(1)

Subjective Probability

183

(1)

Probability and Risk Taking

184

(5)

The Addition Rules for Probability

189

(10)

The Multiplication Rules and Conditional Probability

199

(13)

The Multiplication Rules

199

(5)

Conditional Probability

204

(3)

Probabilities for ``At Least''

207

(5)

Counting Rules

212

(11)

The Fundamental Counting Rule

212

(3)

Factorial Notation

215

(1)

Permutations

215

(2)

Combinations

217

(6)

Probability and Counting Rules

223

(4)

Summary

227

(10)

Discrete Probability Distributions

237

(48)

Introduction

238

(1)

Probability Distributions

239

(6)

Mean, Variance, Standard Deviation, and Expectation

245

(11)

Mean

245

(3)

Variance and Standard Deviation

248

(2)

Expectation

250

(6)

The Binomial Distribution

256

(13)

Other Types of Distributions (Optional)

269

(9)

The Multinomial Distribution

269

(1)

The Poisson Distribution

270

(2)

The Hypergeometric Distribution

272

(6)

Summary

278

(7)

The Normal Distribution

285

(62)

Introduction

286

(2)

Properties of a Normal Distribution

288

(2)

The Standard Normal Distribution

290

(17)

Finding Areas Under the Standard Normal Distribution Curve

291

(8)

A Normal Distribution Curve as a Probability Distribution Curve

299

(8)

Applications of the Normal Distribution

307

(15)

Finding Data Values Given Specific Probabilities

311

(2)

Determining Normality

313

(9)

The Central Limit Theorem

322

(9)

Distribution of Sample Means

322

(6)

Finite Population Correction Factor (Optional)

328

(3)

The Normal Approximation to the Binomial Distribution

331

(7)

Summary

338

(9)

Confidence Intervals and Sample Size

347

(44)

Introduction

348

(1)

Confidence Intervals for the Mean (σ Known or n ≥ 30) and Sample Size

349

(13)

Confidence Intervals

350

(5)

Sample Size

355

(7)

Confidence Intervals for the Mean (σ Unknown and n < 30)

362

(7)

Confidence Intervals and Sample Size for Proportions

369

(8)

Confidence Intervals

370

(1)

Sample Size for Proportions

371

(6)

Confidence Intervals for Variances and Standard Deviations

377

(7)

Summary

384

(7)

Hypothesis Testing

391

(72)

Introduction

392

(1)

Steps in Hypothesis Testing--Traditional Method

393

(12)

z Test for a Mean

405

(14)

P-Value Method for Hypothesis Testing

410

(9)

t Test for a Mean

419

(10)

z Test for a Proportion

429

(8)

Χ2 Test for a Variance or Standard Deviation

437

(12)

Additional Topics Regarding Hypothesis Testing

449

(4)

Confidence Intervals and Hypothesis Testing

449

(2)

Type II Error and the Power of a Test

451

(2)

Summary

453

(10)

Testing the Difference Between Two Means, Two Variances, and Two Proportions